The numerical solution of second-order boundary value problems on nonuniform meshes
Mathematics of Computation
High order finite volume approximations of differential operators on nonuniform grids
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Fully conservative higher order finite difference schemes for incompressible flow
Journal of Computational Physics
Conservative high-order finite-difference schemes for low-Mach number flows
Journal of Computational Physics
Journal of Computational Physics
High order finite difference schemes on non-uniform meshes with good conversation properties
Journal of Computational Physics
Journal of Computational Physics
A Volume-of-Fluid based simulation method for wave impact problems
Journal of Computational Physics
A staggered compact finite difference formulation for the compressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Higher-order mimetic methods for unstructured meshes
Journal of Computational Physics
The numerical simulation of liquid sloshing on board spacecraft
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A fixed-mesh method for incompressible flow-structure systems with finite solid deformations
Journal of Computational Physics
Improving shock-free compressible RANS solvers for LES on unstructured meshes
Journal of Computational and Applied Mathematics
Symmetry-preserving upwind discretization of convection on non-uniform grids
Applied Numerical Mathematics
Multigrid relaxation methods for systems of saddle point type
Applied Numerical Mathematics
Stability of central finite difference schemes on non-uniform grids for the Black--Scholes equation
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Stabilization of the Eulerian model for incompressible multiphase flow by artificial diffusion
Journal of Computational Physics
Applied Numerical Mathematics
Comparison of some Lie-symmetry-based integrators
Journal of Computational Physics
What does Finite Volume-based implicit filtering really resolve in Large-Eddy Simulations?
Journal of Computational Physics
Parallel direct Poisson solver for discretisations with one Fourier diagonalisable direction
Journal of Computational Physics
Computers & Mathematics with Applications
When Does Eddy Viscosity Damp Subfilter Scales Sufficiently?
Journal of Scientific Computing
Error-Landscape Assessment of Large-Eddy Simulations: A Review of the Methodology
Journal of Scientific Computing
Journal of Computational Physics
A Robust Two-Level Incomplete Factorization for (Navier-)Stokes Saddle Point Matrices
SIAM Journal on Matrix Analysis and Applications
Energy-conserving Runge-Kutta methods for the incompressible Navier-Stokes equations
Journal of Computational Physics
An energy preserving formulation for the simulation of multiphase turbulent flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Symmetry-preserving discretization of Navier-Stokes equations on collocated unstructured grids
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.59 |
We propose to perform turbulent flow simulations in such manner that the difference operators do have the same symmetry properties as the underlying differential operators, i.e., the convective operator is represented by a skew-symmetric coefficient matrix and the diffusive operator is approximated by a symmetric, positive-definite matrix. Mimicking crucial properties of differential operators forms in itself a motivation for discretizing them in a certain manner. We give it a concrete form by noting that a symmetry-preserving discretization of the Navier-Stokes equations is stable on any grid, and conserves the total mass, momentum and kinetic energy (for the latter the physical dissipation is to be turned off, of coarse). Being stable on any grid, the choice of the grid may be based on the required accuracy solely, and the main question becomes: how accurate is a symmetry-preserving discretization? Its accuracy is tested for a turbulent flow in a channel by comparing the results to those of physical experiments and previous numerical studies. The comparison is carried out for a Reynolds number of 5600, which is based on the channel width and the mean bulk velocity (based on the channel half-width and wall shear velocity the Reynolds number becomes 180). The comparison shows that with a fourth-order, symmetry-preserving method a 64 × 64 × 32 grid suffices to perform an accurate numerical simulation.